Chemical transformations, to a greater or lesser extent, result in a mixture of products and purification of the desired product is often achieved by crystallisation. Purification by crystallisation relies on preferential dissolution of a portion of the sample containing the unwanted components, along with a quantity of the desired component. The amount of desired component lost during this purification process is of particular importance in an industrial or commercial context and it would clearly be desirable to minimise the losses of desired components.
One example of a multicomponent mixture that is likely to require separation into its constituents is a stereoisomeric system involving chiral centres. In a stereoisomeric system, the number of possible stereoisomers for any given compound is 2n, where n is the number of asymmetric atomic centres. Thus, a system with two chiral centres provides four possible stereoisomers (notwithstanding the possibility of the optionally inactive meso form). Three chiral centres would give eight possible stereoisomers, and so on.
In many chemical reactions in which chirality is an issue, stereoisomeric purity is less than perfect. It may be that stereochemical corruption occurs during processing, that the selectivity of the process is less than optimal, or simply that the optical purity of the starting materials is low. In any case, the end result is that the products of the reaction are contaminated with unwanted stereoisomers.
Historically, removal of the unwanted stereoisomers has been achieved by crystallisation and, although modern techniques such as Simulated Moving Bed Chromatography are gaining acceptance, it is likely that crystallisation will remain the dominant method of purification for the foreseeable future.
In view of the foregoing and the fact that the historical approach relied on a series of “trial and error” experiments, and particularly because of the demand of the pharmaceutical industry for chiral products of high stereochemical purity coupled with the increase in the number of chiral pharmaceutical agents, a method for calculating the maximum yield from a multicomponent mixture of stereoisomers was developed. This method is described in Tetrahedron: Asymmetry 9 (1998), 2925–2937. Of course the demands of the pharmaceutical industry in this regard are also becoming increasingly important in other technical areas, such as the fine chemical, agrochemical and electronics markets.
The approach is based on, but not restricted to, the Ideal approximation. For optimal recovery, it is necessary to dissolve no more of the sample than the maximum amount of material in the sample having a composition corresponding to the eutectic. Therefore, the basis of estimating the maximum recovery of pure component from the mixture by crystallisation requires knowledge of the composition of the eutectic. In the first instance, it is assumed that the eutectic is not influenced to an appreciable degree by the solvent. It is reckoned that this is a reasonable approximation in the case of stereoisomers, since these have the same functionality arranged on a very similar skeleton, so differences in influences of the solvent between the isomers will be minimal.
In the first instance, it is also assumed that the system behaves as a conglomerate, as described by the Shroeder-Van Laar equation. A conglomerate is a mechanical mixture of enantiomeric crystals which are resolvable by entrainment or triage.
In the non-ideal case, if more than one isomer type crystallises in the unit cell, for example in the case of a racemic compound, the Prigogine-Defay equation can be applied. Determination of the optimal yield based on this approach requires the following information:                the melting point of each component;        the heat of fusion of each component;        determination of conglomerate or racemic compound behaviour, and        the initial composition of the mixture.        
These may then be derivatised, for example as salts, esters or the like, depending on the molecular functionality. Their melting points and heats of fusion are subsequently determined, using differential scanning calorimetry (DSC) followed by calculation of the maximum theoretical yield. Although this process can be simplified using automated systems, it still represents a significant up-front overhead of:                isomer separation;        preparation of derivatives of each isomer;        determination of the nature of the crystal form—are they        
conglomerates or racemic compounds?
Whilst this approach, for the first time, provided the basis for a rational evaluation of the purification process in multicomponent systems, it suffers from the limitation of requiring separation of the stereoisomers.
Moreover, there are inherent limitations due to the possibility of thermal instability of the materials, making DSC analysis unreliable. Additionally, the fact that the derivatives are prepared separately may introduce the possibility of polymorph formation which would not otherwise occur in crystallisation of the mixture. This can lead to errors in subsequent measurements and calculation.
It is therefore an object of the present invention to provide a means for determining the optimal yield for obtaining a purified product from a multicomponent system that avoids the above problems.